CN110135499A - Clustering method based on the study of manifold spatially adaptive Neighborhood Graph - Google Patents
Clustering method based on the study of manifold spatially adaptive Neighborhood Graph Download PDFInfo
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Abstract
A kind of clustering method that the adaptive neighborhood graphics based on manifold space is practised, there is the multidimensional data of complex nonlinear structure for image and video etc., traditional Spectral Clustering constrains the similitude between learning data using Laplce, the problem of be easy to causeing misinterpretation data global structure, it is established in Grassmann manifold based on adaptive neighborhood regularization is introduced from after the Unified frame of expression, thus to improve the clustering performance to video or image set multidimensional data.The present invention relates to manifold learning, the fields such as pattern-recognition and machine learning are significantly better than other classical clustering methods depending on Clustering Effect towards image and the more of video high dimensional data, effectively improve recognition capability.
Description
Technical field
The present invention relates to manifold learning, the fields such as pattern-recognition and machine learning, especially towards image, video multidimensional number
According to cluster task.
Background technique
With the fast development of internet and cloud computing technology, the multidimensional datas such as image, the video of magnanimity are by wide in real time
General propagation and storage, in addition to small part data have the personalized label of user, what is do not marked mostly is unordered
Figure or video sequence, manually mark its classification information inefficiency and need to pay high cost, cause " there are data, it is difficult
Using " predicament.Therefore, how big in face of these scale of constructions, variation multiplicity non-linear multidimensional data, carry out efficient earth's surface to it
It reaches, excavates the semantic informations information such as the classification being hidden in data, be the ultimate challenge that current the field of data mining faces, this
The manifold that the solution of problem depends on high dimensional data indicates and the breakthrough of clustering method.
The present age is based on the Spectral Clustering from expression, it is therefore an objective to which study accurately reflects the affine square of similitude between data
Battle array is generally used the European measurement of initial data when describing similitude, and is usually constrained using Laplce so that affine
The global structure of matrix holding initial data.However, there are two disadvantages: firstly, these methods be mainly designed for Europe it is several in
Vector data in moral space is not particularly suited for the multidimensional data with non-linearity manifold structure, such as video and image set.Its
Secondary, clustering performance is largely dependent upon the quality of the Laplacian Matrix learnt in advance, and wherein global structure may quilt
Misinterpretation is without considering various structures.
Summary of the invention
The high dimensional data problem is clustered to solve conventional method, the invention discloses kind of a popular world adaptive neighborhoods
The clustering method that graphics is practised.It is established in Grassmann manifold based on introducing adaptive neighborhood after the Unified frame of expression certainly just
Then change thus to improve the clustering performance to video or image set multidimensional data.Model in this method direct solution manifold is asked
Topic, in the optimal solution of Euclidean space search symmetrical matrix linear combination, to simplify learning process, significant effect is better than other
Classical clustering method.
Specific technical solution is as follows:
Image/video etc. is not suitable for complex nonlinear knot for the measure of this linear space of Euclidean distance
The problem of high dimensional data of structure, since these multidimensional datas can be embedded in low dimensional manifold, it is more to disclose these for we first
The non-linearity manifold structure of dimension data behind realizes abstract stream for based on Grassmann manifold is introduced from the learning method of expression
Then shape frame introduces adaptive neighborhood regularization on this basis to learn new neighborhood relationships from coefficient matrix.Finally will
The coefficient matrix and adaptive figure learnt executes spectral clustering (Ncut) operation, obtains more views cluster knot of video and image set
Fruit, to improve clustering precision and recognition capability.
It is to the present invention, especially to the explanation based on the adaptive neighborhood graphics learning method from expression below:
Directly learn the structural information (i.e. Laplacian Matrix) come self initial data for conventional method, we will be based on
Introduce Grassmann manifold from the learning method of expression, realize introduce after abstract manifold frame adaptive neighborhood regularization with from
Coefficient matrix learns new neighborhood relationships.
(1) by Euclidean space based on the study formula from expression:
It expands in manifold to establish in Grassmann manifold based on the study from expression:
Wherein one group of Grassmann point χ={ X1,X2,...XN},Xi∈g(p,d)。zijIndicate XiAnd XjBetween it is similar
Property, ziFor XiNew expression
(2) basis:The mapping distance of middle Grassmann manifold embodies mould
Abstract manifold distance in type.That is:
The Grassmann point of mapping has form identical with positive definite matrix, the abstract line in manifold in Sym (d)
Property combinatorial operation indicate are as follows:WhereinIndicate three ranks
Tensor, it includes all mapping symmetrical matrixes.Therefore, we can be rebuild in Grassmann manifold based on the study from expression
Model is as follows:
Reconstructed error ε is also 3 rank tensors.
(3) adaptive neighborhood regularizationIt is a kind of adaptive learning
The good strategy of figure, it reflects the neighborhood relationships between data, and the constant drawing learnt in advance rather than from initial data is general
Lars matrix.The present invention learns to indicate { z using this method1,...,zNNeighborhood relationships, rather than original Grassmann number
According to { X1,X2..., XN, a new adaptive neighborhood form is reconfigured to be write as:
Above-mentioned adaptive neighborhood regularization is substituted into method proposed by the present invention, obtains final objective function:
Here it is GMAN.
(4) point in some manifolds is given, such as the subspace of identical dimensionals some in Euclidean space, then clustering in manifold
Task refer to through the similitude between measurement sample, all given points (subspace) are clustered into some clusters.It is solving
(3) after, we can obtain the subspace representing matrix Z learnt from initial data and the adaptive neighborhood learnt from Z simultaneously
Figure A. matrix Z and A reflects the similitude between data, is used directly for executing K-means or NCut.In experiment respectively
(| Z |+| Z |TThe He of)/2Upper execution NCut is to obtain cluster result.
Beneficial effect
Face-image clustering face cluster is a basic problem of area of pattern recognition, experiments have shown that the present invention is not only
Good Clustering Effect can be shown to sets of video data to facial data set, and also, greatly improve recognition capability.
Detailed description of the invention
Fig. 1, the method for the present invention flow chart；
Fig. 2, Extended YaleB data set；
Fig. 3, CMUPIE data set；
Fig. 4, UCF sports video data collection；
Fig. 5, ballet action video；
Fig. 6, traffic highway sets of video data；
Specific embodiment
Face-image clustering-face cluster is a basic problem of area of pattern recognition.This is used in the present embodiment
Invention clusters on two image sets, is finally completed and clusters task to more views of image data, and in this experiment, we use
Two common face data collection, including Extended YaleB and CMUPIE, to construct set of face images data.Furthermore in order to
Illustrate that the present invention equally can handle video, therefore also select three groups of video datas, using the present invention for solving higher-dimension video
Data regard the problem of cluster more.Furthermore in order to illustrate effectiveness of the invention, comparative experiments also has been carried out with other clustering algorithms.
Process frame of the present invention is as shown in Figure 1:
We use two face image data collection (Fig. 2, Extended YaleB and Fig. 3, CMUPIE), two movement views
Frequency data set (Fig. 4, UC exercise data collection and Fig. 5, entrechat data set) and a traffic scene sets of video data construct
Input sample point (Fig. 6, traffic highway sets of video data).Operating process is as follows:
SVD decomposition is executed after image, video set data are extracted feature first, is then denoted as a series of
Grassmann manifold point form: { X1、X2、…、XN, as input data sample point；
Then it by being handled based on the adaptive neighborhood graphics learning method from expression input data, obtains optimization and asks
Subspace representing matrix Z and adaptive neighborhood figure A after solution, wherein the adaptive neighborhood graphics habit side based on expression certainly
Method model is as follows:
Wherein, the i-th row jth of matrix Z is classified as zij, it indicates data point XiAnd XjBetween similitude
LAIt is the Laplacian Matrix of figure A, adaptive neighborhood figure A equally reflects the similitude between data sample
For ‖ Z ‖l, the nuclear norm of matrix Z, F norm and l are taken in experiment respectively1Norm calculates separately result
Three rank tensor ε are the reconstructed errors during the expression of subspace, | | | |FIndicate F norm, the mark of tr representing matrix
Weighting factor λ1λ2λ3Value range is { 10-4, 10-3, 10-2, 10-1, 100, 101, 102, 103Three rank tensors×3Indicate the product of mould -3；
The subspace representing matrix Z and adaptive figure A finally obtained according to Optimization Solution, carries out spectral clustering to it respectively
Ncut operation, obtains subspace clustering result；
It is noted that the clustering method of comparative approach LRR, SSC, LS3C and LRSR based on vector data, therefore we pass through
The high-dimensional of these long vectors is reduced to low dimensional by PCA, and each video/image set vector is then turned to input.
In order to verify the superiority of GMAN, we are by itself and SCGSM, FGLRR, LapFGLRR, CascadedGLRR, LRR,
Several classical clustering methods of SSC, LS3C and LRSR are compared.Table 1 is that the input data of comparative approach indicates.
Table 1: the input data type of all comparative approach
Needle can be effectively improved in order to verify the adaptive neighborhood graphics learning method proposed by the invention based on from expression
To more view clustering performances of high dimensional data, this experiment carries out son on two face data collection Extended Yale B and CMUPI
Space clustering.Table 2 is the experimental result of the subspace clustering of the two face data collection compared with other clustering methods.Wherein
GMAN-Z and GMAN-A is respectively indicated to sub- space representation matrix Z and adaptive neighborhood figure A execution spectral clustering operation, GMAN-Nu,
GMAN-F, GMAN-1 are respectively indicated in method model to matrix Z using nuclear norm, F norm, the obtained more view clusters of 1 norm
As a result.
In order to assess clustering method from different aspect, we have selected five kinds of canonical measures, i.e. accuracy (ACC), standard
Mutual information (NMI), blue moral index (RI), purity (purity) and F index (FM), the high value of these indexs can reflect more preferably
Clustering performance.
Table 2: the subspace clustering result on face data collection
Can be seen that from the experimental result of table 2 it is proposed that method, especially GMAN-Nu can obtain satisfactory
Cluster result.Most of clustering methods based on Grassmann manifold better than based on vector data method (SSC, LRR and
LS3C), this shows that Grassmann manifold can extract more discriminant informations from image set data；It is important as one
Baseline, FGLRR cluster result ratio SCGSM is more preferable, demonstrates the advantage based on the learning method from expression；In addition, for GMAN-
The clustering performance of Nu, GMAN-F and GMAN-1, adaptive neighborhood figure A are better than coefficient matrix Z, and which reflects adaptive learning neighborhoods
Superiority of the relationship to image set data.
Therefore, we conclude that, it is proposed by the invention towards manifold based on from expression adaptive neighborhood graphics
Learning method can effectively solve more view clustering problems of high dimensional image, promote facial recognition capability.
In order to which the method for further proving us can also show good clustering performance to higher-dimension video data, selection
Two corresponding action video data sets: UCF exercise data collection and entrechat data set and a traffic scene video data
Collection, in these three sets of video data use it is proposed that based on from expression adaptive neighborhood graphics learning method it is carried out
Cluster operation.Table 3 and table 4 show corresponding cluster results.
Table 3: the subspace clustering result on action video data set
Table 4: the subspace clustering result on traffic video data set
Change from can be seen that more than table 3UCF and entrechat sets of video data depending on cluster result in extensive and class
Challenge, it is proposed that GMAN-Nu and GMANF still maintain relatively excellent clustering performance, be more than the side of all comparisons
Method.And GMAN-Nu-Z have it is more preferable than baseline FGLRR effect than GMAN-Nu-A better performance and GMAN-Nu-Z, this
Mean that adaptive neighborhood figure A has positive-effect to coefficient matrix Z in optimization process.Likewise, 4 traffic scene video counts of table
Shown according to the experimental result of collection, it is proposed that all methods all than other comparative approach have higher clustering precision, especially
It is that accuracy improves 95% or more.
To which we from which further follow that conclusion, the cluster proposed by the present invention based on the study of manifold spatially adaptive Neighborhood Graph
Method can efficiently accomplish the cluster task of the high dimensional data image and video for complex nonlinear structure, have good
Application prospect.
Claims (1)
1. the high dimensional data figure based on the clustering method of manifold spatially adaptive Neighborhood Graph study, suitable for complex nonlinear structure
Picture or video, it is characterised in that the following steps are included:
(1) it constructs sample number and is the image data set of N, and be denoted as a series of Grassmann manifold point { X1、X2、…、
XN, as input data sample point；
(2) by being handled based on the adaptive neighborhood graphics learning method from expression input data, after obtaining Optimization Solution
Subspace representing matrix Z and adaptive neighborhood figure A, wherein described based on the adaptive neighborhood graphics learning method mould from expression
Type is as follows:
Wherein, the i-th row jth of matrix Z is classified as zij, it indicates data point XiAnd XjBetween similitude, for ‖ Z ‖lSquare can be taken
The nuclear norm of battle array Z, F norm and l1Norm calculate separately as a result, three rank tensor ε be subspace expression during reconstructed error, |
|·||FIndicate F norm, the mark of tr representing matrix, LAIt is the Laplacian Matrix of figure A, adaptive neighborhood figure A equally reflects data
Similitude between sample, weighting factor λ1、λ2λ3, value range be { 10-4, 10-3, 10-2, 10-1, 100, 101, 102, 103, three
Rank tensor×3Indicate the product of mould -3；
(3) the subspace representing matrix Z and adaptive figure A obtained according to Optimization Solution, carries out spectral clustering Ncut behaviour to it respectively
Make, obtains subspace clustering result.
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